The manager of a grocery store believes that the number of people waiting in the express check out lane follows a Poisson distribution.While watching the lane at random times throughout the day and week, she collects the following information. $\begin{array}{|l|r|r|r|r|r|r|}
\hline \begin{array}{l}
\text { People waiting in express } \
\text { check out lane }
\end{array} & 0 & 1 & 2 & 3 & 4 & \geq 5 \
\hline \text { Observed frequency } & 35 & 41 & 22 & 14 & 3 & 2\
\hline
\end{array}$

Using $\alpha$=0.10, the appropriate decision for this goodness of fit test is _______.
A)do not reject the null hypothesis that the observed distribution is Poisson
B)reject the null hypothesis that the observed distribution is not the Poisson
C)do nothing
D)do not reject the null hypothesis that the observed distribution is not Poisson
E)reject the null hypothesis that the observed distribution is Poisson

Question

The manager of a grocery store believes that the number of people waiting in the express check out lane follows a Poisson distribution.While watching the lane at random times throughout the day and week, she collects the following information. $\begin{array}{|l|r|r|r|r|r|r|}
\hline \begin{array}{l}
\text { People waiting in express } \
\text { check out lane }
\end{array} & 0 & 1 & 2 & 3 & 4 & \geq 5 \
\hline \text { Observed frequency } & 35 & 41 & 22 & 14 & 3 & 2\
\hline 
\end{array}$

Using $\alpha$=0.10, the appropriate decision for this goodness of fit test is _______.
A)do not reject the null hypothesis that the observed distribution is Poisson
B)reject the null hypothesis that the observed distribution is not the Poisson
C)do nothing
D)do not reject the null hypothesis that the observed distribution is not Poisson
E)reject the null hypothesis that the observed distribution is Poisson

Quizplus · Accepted Answer

To determine if the observed distribution fits a Poisson distribution, a goodness of fit test is used. Without calculating the exact p-value or chi-square statistic here, the decision to "do not reject the null hypothesis" typically means that the observed frequencies are not significantly different from the expected frequencies under a Poisson distribution, given the chosen significance level (α=0.10). This choice suggests that the data does not provide enough evidence to conclude that the distribution of people waiting in the express checkout lane is not Poisson.

The Manager of a Grocery Store Believes That the Number